Quasi-linear elliptic equations with superlinear convection

TL;DR

This paper investigates the existence and regularity of solutions to quasi-linear elliptic equations with superlinear convection, extending previous results to include p-Laplacian operators and more general conditions.

Contribution

It generalizes earlier findings by analyzing a broader class of quasi-linear elliptic equations with superlinear convection terms, including the p-Laplacian.

Findings

Established existence of solutions under new conditions.

Proved regularity results for solutions with superlinear convection.

Extended previous work to more general operators and growth conditions.

Abstract

We discuss the existence and regularity of solutions to a quasi-linear elliptic equation involving a Leray-Lions operator and a convection term with superlinear growth. In particular, equations involving the p-Laplacian are covered. This paper generalizes some of the results in Boccardo et al. (2024).